Self-interaction of Brownian particles coupled with thermodynamic processes

Biler, Piotr; Krzywicki, A.; Nadzieja, Tadeusz

doi:10.1016/s0034-4877(99)80005-6

Cited by 29 publications

(26 citation statements)

References 9 publications

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“…Such equations can be derived from a microscopic model involving Brownian particles and heat particles modeled as quantum oscillators. A generalization of these equations for self-gravitating Brownian particles has been proposed by Biler et al [18]. It consists of the Smoluchowski-Poisson system (6) (5) coupled to a diffusion equation for the temperature…”

Section: 1 the Smoluchowski-poisson Systemmentioning

confidence: 99%

Thermodynamics of self-gravitating systems

2002

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We study the thermodynamics and the collapse of a self-gravitating gas of Brownian particles. We consider a high-friction limit in order to simplify the problem. This results in the Smoluchowski-Poisson system. Below a critical energy or below a critical temperature, there is no equilibrium state and the system develops a self-similar collapse leading to a finite time singularity. In the microcanonical ensemble, this corresponds to a "gravothermal catastrophe" and in the canonical ensemble to an "isothermal collapse." Self-similar solutions are investigated analytically and numerically.

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Section: 1 the Smoluchowski-poisson Systemmentioning

confidence: 99%

Thermodynamics of self-gravitating systems

2002

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“…We are interested in the motion of a system of Brownian particles confined to a thermally insulated container Ω ⊂ R n (n = 2, 3). We assume that the particles move under the influence of mutual electric or gravitational interactions and are submitted to thermal diffusion (for physical background see [2], [8]). …”

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confidence: 99%

“…It is known ( [2]; [3], Ch. 10) that in the thermodynamical equilibrium the electric (gravitational) potential Φ of the system under consideration satisfies the Poisson-Boltzmann equation…”

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Radially symmetric solutions of the Poisson-Boltzmann equation with a given energy

Nadzieja

Raczyński

2000

Appl. Math. (Warsaw)

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“…It describes also the evolution of density and temperature of a self-attracting cluster of Brownian particles in a ball of R 3 in the limit of infinite thermal conductivity (see e.g. [1], [4] and [7]). Here, τ > 0 is time, x is the spatial variable, n stands for the density, ψ is the gravitational potential (defined by (1.2), (1.4)), E is the total energy, which is assumed to be constant, and θ is the (uniform) temperature.…”

Section: Introduction Let B Denote the Open Ball In Rmentioning

confidence: 99%